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Highlights of Calculus is a series of short videos that introduces the basic ideas of calculus — how it works and why it is...
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Highlights of Calculus is a series of short videos that introduces the basic ideas of calculus — how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.In addition to the videos, there are summary slides and practice problems complete with an audio narration by Professor Strang. You can find these resources to the right of each video.This resource is also available on Highlights for High School.About the InstructorProfessor Gilbert Strang is a renowned mathematics professor who has taught at MIT since 1962. Read more about Prof. StrangAcknowledgementsSpecial thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.

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This is a free online course offered by the Saylor Foundation.'“Everything is numbers.” This phrase was uttered by the lead...
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This is a free online course offered by the Saylor Foundation.'“Everything is numbers.” This phrase was uttered by the lead character, Dr. Charlie Epps, on the hit television show “NUMB3RS.” If everything has a mathematical underpinning, then it follows that everything is somehow mathematically connected, even if it is only in some odd, “six degrees of separation (or Kevin Bacon)” kind of way.Geometry is the study of space (for now, mainly two-dimensional, with some three-dimensional thrown in) and the relationships of objects contained inside. It is one of the more relatable math courses, because it often answers that age-old question, “When am I ever going to use this in real life?” Look around you right now. Do you see any triangles? Can you spot any circles? Do you see any books that look like they are twice the size of other books? Does your wall have paint on it?In geometry, you will explore the objects that make up our universe. Most people never give a second thought to how things are constructed, but there are geometric rules at play. Most people never think twice about a rocket launch, but if that rocket is not launched at an exact angle, it will miss its target. A football field has to be measured out to be a rectangle; if you used another shape, such as a trapezoid, that would give an unfair advantage to one team, because that one team would have more space to work with.In this course, you will study the relationships between lines and angles. Have you ever looked at a street map? Believe it or not, there is a lot of geometry on a map, as you will see from this course. You will learn to calculate how much space an object covers, which is useful if you ever have to, say, buy some paint. You will learn to determine how much space is inside of a three-dimensional object, which is useful for those times you are trying to fit four suitcases, three kids, two adults, and a dog into the back of your vehicle.These are just some of the topics you will be learning. As you will quickly see, everything is not just numbers; it is also relationships. Even nature itself knows this. What did the little acorn say when it grew up? “Gee, I’m a tree!”'

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This online course comes from the Open Learning Initiative (OLI) by Carnegie Mellon. “The course includes self-guiding...
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This online course comes from the Open Learning Initiative (OLI) by Carnegie Mellon. “The course includes self-guiding materials and activities, and is ideal for independent learners, or instructors trying out this course package.”״This course introduces students to the basic concepts, logic, and issues involved in statistical reasoning. Major topics include exploratory data analysis, an introduction to research methods, probability, and statistical inference. The objectives of this course are to give students confidence in manipulating and drawing conclusions from data and provide them with a critical framework for evaluating study designs and results.An important feature of the course is the use of an intelligent tutoring system developed at Carnegie Mellon called "StatTutor." StatTutor aims to facilitate understanding of statistical ideas and analytical techniques by helping students construct useful knowledge representations and thereby develop effective problem-solving skills. It uses a specified outline of steps to follow in solving problems, or "scaffolding״. StatTutor will use scaffolding and immediate feedback flexibly, tracking and responding to individual students as they navigate the learning environment.״

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Calculators can perform math functions quickly and easily. The most common functions are addition, subtraction,...
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Calculators can perform math functions quickly and easily. The most common functions are addition, subtraction, multiplication, and division. This course will use the Touch Method, which means using the calculator without looking at the keys. Using this method will help develop competency. After building competency, students will be able to use 10-key calculators to enter numeric data and perform calculations efficiently.

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The study of "abstract algebra" grew out of an interest in knowing how attributes of sets of mathematical objects behave when...
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The study of "abstract algebra" grew out of an interest in knowing how attributes of sets of mathematical objects behave when one or more properties we associate with real numbers are restricted. The student will begin this course by reviewing basic set theory, integers, and functions in order to understand how algebraic operations arise and are used. The student then will proceed to the heart of the course, which is an exploration of the fundamentals of groups, rings, and fields. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 231)

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This course contains both content that reviews or extends concepts and skills learned in previous grades and new, more...
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This course contains both content that reviews or extends concepts and skills learned in previous grades and new, more abstract concepts in algebra. Students will gain proficiency in computation with rational numbers (positive and negative fractions, positive and negative decimals, whole numbers, and integers) and algebraic properties. New concepts include solving two-step equations and inequalities, graphing linear equations, simplifying algebraic expressions with exponents, i.e. monomials and polynomials, factoring, solving systems of equations, and using matrices to organize and interpret data

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This is a free online course offered by the Saylor Foundation.'Calculus can be thought of as the mathematics of CHANGE....
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This is a free online course offered by the Saylor Foundation.'Calculus can be thought of as the mathematics of CHANGE. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently CONSTANT. Solving an Algebra problem, like Y = 2X + 5, merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate R, such as Y = X0+Rt where t is elapsed time and X0 is the initial deposit. But with compounded interest, now things get complicated for algebra as the rate R is now itself a function of time with Y = X0+ R(t)t. Now we have a rate of change which itself is changing. Calculus “to the rescue,” as Isaac Newton introduced the world to mathematics specifically designed to handle “those things that change.” Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences, including physical, biological, social, economic, and engineering. However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will learn in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications and many of them will be saved for future courses you might take. This course is divided into four learning sections, or units, plus a reference section, or Appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding “limits” could not be more important as that topic really begins the study of calculus. The third unit will introduce and explain derivatives. With derivatives we are now ready to handle all those “things that change” mentioned above. The fourth unit makes “visual sense” of derivatives by discussing derivatives and graphs. Finally, the fifth unit provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over.'

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This complete course in Calculus for beginners is one of MIT's OpenCourseWare offerings. It includes nearly a dozen Java...
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This complete course in Calculus for beginners is one of MIT's OpenCourseWare offerings. It includes nearly a dozen Java applets to illustrate some of the concepts covered; there is a corresponding set of Flash applets with accompanying audio.

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